Which of the following is an equivalent expression to 81^−1/2?

Question

Responses

181√
the fraction with numerator 1 and denominator square root of 81 - not selected, this is the correct answer

−181√
negative the fraction with numerator 1 and denominator square root of 81 - no response given

81−−√
square root of 81 - no response given

−81−−√

Answer 1

To simplify \( 81^{-1/2} \), you can use the properties of exponents:

1. The negative exponent indicates a reciprocal, so \( 81^{-1/2} = \frac{1}{81^{1/2}} \).
2. \( 81^{1/2} \) is the square root of 81, which is 9.

Putting it all together,

\[ 81^{-1/2} = \frac{1}{81^{1/2}} = \frac{1}{\sqrt{81}} = \frac{1}{9}. \]

Thus, the equivalent expression is the fraction with numerator 1 and denominator square root of 81, which is correct.